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Limit Comparison Test

  1. Jan 9, 2015 #1
    In my textbook it says if you are comparing limn->infinity of an/bn an>0 and bn>0 for the limit comparison test to apply.

    It says nothing about "an" having to be greater than "bn", so as long as both are positive for each term I can use the limit comparison test right? It isn't like the direct comparison test where you need to worry about having all of a sequence's terms be larger/smaller than the one you are comparing to?

  2. jcsd
  3. Jan 9, 2015 #2


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    If an/bn -> 0, you know very little about bn if you are using an as a comparison.
  4. Jan 12, 2015 #3


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    Right. The limit comparison test tells you if the two sequences have the same sort of behavior when n gets large. You don't need one sequence to be greater than or less than the other to see if they behave similarly for large n.
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